use synthetic division to solve $(2x^{3}+4x^{2}-35x + 15)div(x - 3)$. what is the quotient?\n$2x^{2}-2x…

Explanation:

Step1: Set up synthetic division

The divisor is $x - 3$, so we use $c=3$. The dividend coefficients are $2,4,-35,15$.

3	2	4	-35	15

Step2: Bring down the first coefficient

Bring down the first coefficient 2.

3	2	4	-35	15
	2

Step3: Multiply and add

Multiply 3 by 2 to get 6, add to 4 to get 10.

3	2	4	-35	15
		6
	2	10

Step4: Repeat multiplication - addition

Multiply 3 by 10 to get 30, add to - 35 to get - 5.

3	2	4	-35	15
		6	30
	2	10	-5

Step5: One - more multiplication - addition

Multiply 3 by - 5 to get - 15, add to 15 to get 0.

3	2	4	-35	15
		6	30	-15
	2	10	-5	0
The numbers 2, 10, - 5 are the coefficients of the quotient polynomial. The quotient is a quadratic polynomial. The quotient is $2x^{2}+10x - 5$.

Answer:

$2x^{2}+10x - 5$